Option 1 states that the focal length of the objective of a microscope is less than the focal length of the eyepiece. This statement is correct. In a microscope, the objective lens is responsible for gathering and focusing the light from the object being observed. It has a shorter focal length in order to produce a magnified image. The eyepiece lens, on the other hand, is responsible for further magnifying the image formed by the objective lens. It has a longer focal length to produce a virtual image that is viewed by the user.
Option 2 states that the minimum distance between an object and its real image formed by a convex lens of focal length f is equal to 4f. This statement is incorrect. The minimum distance between the object and its real image formed by a convex lens is given by the formula:
1/f = 1/v - 1/u
Where f is the focal length, v is the image distance, and u is the object distance. This formula shows that the distance between the object and the real image depends on both the focal length and the distances. It is not equal to 4f.
Therefore, only statement 1 is correct, and the correct answer is option 3.